Research

Research Interests

My research interests lie in noncommutative geometry and global geometric analysis, in particular:

  • Yang-Mills theory in noncommutative geometry; moduli spaces of instantons on noncommutative four-manifolds;
  • noncommutative geometry of quantum groups and their homogeneous spaces;
  • complex structures on noncommutative homogeneous spaces; noncommutative twistor theory;
  • unbounded (i.e. constructive) KK-theory and applications;
  • applications of operator spaces in noncommutative geometry.

Publications

In reverse chronological order of writing:

  • Operator Spaces and Noncommutative Geometry in Interaction (with Magnus Goffeng, Jens Kaad and Bram Mesland, Eds.)
    Oberwolfach Reports 13 (2016, 267–295 (29pp)
  • Gauge Theory for Spectral Triples and the Unbounded Kasparov Product (with Bram Mesland and Walter D. van Suijlekom).
    J. Noncommut. Geom. 10 (2016), 135–206 (72pp)
  • The Gysin Sequence for Quantum Lens Spaces (with Francesca Arici and Giovanni Landi).
    J. Noncommut. Geom. 9 (2015), 1077–1111 (35pp)
  • The Noncommutative Topology of Anti-Self-Dual Gauge Fields.
    J. Geom. Phys. 72 (2013), 34–53 (20pp)
  • Moduli Spaces of Instantons on Toric Noncommutative Manifolds (with Giovanni Landi and Walter D. van Suijlekom),
    Adv. Theor. Math. Phys. 17 (2013), 1129–1193 (65pp)
  • Differential and Twistor Geometry of the Quantum Hopf Fibration (with Giovanni Landi).
    Commun. Math. Phys. 315 (2012), 489–530 (41pp)
  • The ADHM Construction of Instantons on Noncommutative Spaces (with Walter D. van Suijlekom).
    Rev. Math. Phys. 23 (2011), 261–307 (47pp)
  • The 3D Spin Geometry of the Quantum Two-Sphere (with Giovanni Landi). Rev. Math. Phys. 22 (2010), 963–993 (31pp)
  • Moduli Spaces of Noncommutative Instantons: Gauging Away Noncommutative Parameters (with Giovanni Landi). Quart. J. Math. 63 (2012), 41–86 (46pp)
  • Families of Monads and Instantons from a Noncommutative ADHM Construction (with Giovanni Landi). In “Quanta of Maths”, a special volume of the Clay Mathematics Institute dedicated to Alain Connes. Clay Math. Proc. 11 (2010), 55–84 (30pp)
  • Quantisation of Twistor Theory by Cocycle Twist (with Shahn Majid). Commun. Math. Phys. 284 (2008), 713–774 (62pp)